Inductive response of HTSC platelets and disks due to AC conductivity analytic theory for axial symmetry

Abstract The electrodynamic boundary-value problem which is basic for the AC penetration depth and conductivity measurement of HTSC samples by means of the mutual-induction technique is re-examined, and novel analytic solutions are presented. In particular, the vector potential from the exciting current in a circular driving loop and its perturbation due to the induced currents in the neighboring HTSC sample is studied, axial symmetry provided. This paper is mainly concerned with arrangements characterized by a strong field perturbation from the sample, combined with a field concentration in certain sample regions, but far from the sample edges, namely disk-shaped samples with radius larger than the driving loop radius. Both the limiting case of the infinite platelet, and/or the AC penetration depth much smaller than the sample thickness (bulk limit) are included. Powerful asymptotic methods are used to evaluate the complicated integral representations for the infinite-platelet problem. Asymptotic methods are also introduced to solve the integral equations for the finite disk. Remainders are given to estimate the correctness of the analytic approximations.